README.md

In thanhuwe8/fineng: What the Package Does (One Line, Title Case)

fineng

The package provides routines to calculate option prices using different closed-form solutions and Monte-Carlo simulations based on different stochastic motions

Installation

You can install the released version of fineng with

devtools::install_github("fineng")

New Updates on February 2019

• Simulation for Contiuous and Discrete Geometric Brownian Motion
• Finite-Difference Approximations, Pathwise derivative and Likelihood Ratio method for Option Greeks
• Control Variates, Antithetic Variates and Stratified Sampling

Plan for development

We plan to add the following features in the next releases:

• Heston Model with Newton-Cotes and Gaussian Quadrature (only Mid-point rule is currently supported)
• Simulation of symmetric random walk, scaled random walk and Jump Diffusion Process.
• Brownian Bridge
• American Option Pricing using Monte Carlo simulation
• Rcpp for high-performance computation.

Usage

Geometric Brownian Motion Simulation

library(fineng)
SinglePath <- SimGBM(100,0.03,0.25,2,100,"discrete")
Path100 <- SimDGBM(100,0.03,0.25,2,100,10,"continuous")
Path100Terminal <- SimTGBM(100,0.03,0.25,2,100,10,"continuous")

head(SinglePath)
#> [1] 100.00000 101.28530 101.27799  98.89855  99.27722  97.31816
knitr::kable(head(Path100,10))

| path1 | path2 | path3 | path4 | path5 | path6 | path7 | path8 | path9 | path10 | | --------: | --------: | --------: | --------: | --------: | --------: | --------: | -------: | --------: | --------: | | 100.00000 | 100.00000 | 100.00000 | 100.00000 | 100.00000 | 100.00000 | 100.00000 | 100.0000 | 100.00000 | 100.00000 | | 96.29663 | 99.42534 | 94.13160 | 101.54419 | 98.40329 | 104.63166 | 97.16100 | 100.0716 | 103.12666 | 99.20133 | | 92.21547 | 97.85912 | 97.65704 | 99.31980 | 100.88840 | 103.08846 | 101.48596 | 106.5623 | 104.12503 | 101.77384 | | 91.27924 | 96.94309 | 98.28728 | 97.13502 | 100.14344 | 105.61552 | 100.86194 | 116.8408 | 99.68115 | 100.45551 | | 93.43147 | 102.23515 | 95.32894 | 99.41128 | 98.47941 | 104.13266 | 93.03570 | 116.9082 | 99.43701 | 105.20229 | | 92.09561 | 99.73503 | 98.25180 | 103.42019 | 94.87310 | 102.62783 | 90.09111 | 111.0743 | 95.96988 | 105.93811 | | 96.40398 | 99.49458 | 99.64422 | 109.19116 | 101.78678 | 94.81191 | 86.06863 | 107.7198 | 95.37261 | 105.54326 | | 93.15126 | 101.00149 | 99.36599 | 111.00723 | 99.15677 | 86.97683 | 85.12907 | 111.2482 | 92.78822 | 107.28712 | | 99.25390 | 105.62658 | 96.95822 | 109.90547 | 100.60062 | 87.78285 | 86.16681 | 116.2061 | 95.69383 | 112.97068 | | 104.28692 | 107.48194 | 98.33510 | 108.13056 | 98.47853 | 87.37106 | 80.07122 | 110.5495 | 94.05884 | 108.14635 |

knitr::kable(Path100Terminal)

| | x | | ------ | --------: | | path1 | 265.63570 | | path2 | 116.49457 | | path3 | 83.07854 | | path4 | 67.96923 | | path5 | 72.54115 | | path6 | 104.51031 | | path7 | 154.80156 | | path8 | 135.12695 | | path9 | 98.19967 | | path10 | 179.37457 |

Heston model

### Necessary Paramters
PutCall <- "Call"
# Option Properties
S = 100
K = 100
tau = 0.5
r = 0.03
q = 0.02
# Heston model Properties
kappa = 0.2
theta = 0.25
sigma = 0.3
lambda = 0
v0 = 0.02
rho = -0.8
# Mid-point Properties
N = 1000
a = 1e-5
b = 100

### Heston Price using Mid-point integration rule
HestonPriceMP(PutCall, S, K, tau, r, q, kappa, theta, sigma, lambda, v0, rho, N, a, b)
#> [1] 4.92679

### Comparison with Black-Scholes model

BlackScholes("Call",S = 100, K = 100, tau = 0.5, r = 0.03, q = 0.02, sigma = 0.3)
#> [1] 8.582082

Citation

• Glasserman, Paul. Monte Carlo methods in financial engineering. Vol.
  1. Springer Science & Business Media, 2013.
• Jäckel, Peter. Monte Carlo methods in finance. J. Wiley, 2002.
• Heston, Steven L. “A closed-form solution for options with stochastic volatility with applications to bond and currency options.” The review of financial studies 6.2 (1993): 327-343.

License

This project is licensed under the GPL3 License

thanhuwe8/fineng documentation built on June 9, 2019, 2:43 p.m.